login
A035979
Number of partitions in parts not of the form 21k, 21k+1 or 21k-1. Also number of partitions with no part of size 1 and differences between parts at distance 9 are greater than 1.
0
0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, 105, 136, 164, 208, 251, 316, 378, 470, 564, 693, 828, 1012, 1204, 1460, 1735, 2088, 2474, 2964, 3498, 4169, 4911, 5823, 6838, 8079, 9459, 11131, 13003, 15243, 17761, 20759, 24123, 28107
OFFSET
1,4
COMMENTS
Case k=10,i=1 of Gordon Theorem.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
FORMULA
a(n) ~ exp(2*Pi*sqrt(n/7)) * sin(Pi/21) / (sqrt(3) * 7^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018
MATHEMATICA
nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(21*k))*(1 - x^(21*k+ 1-21))*(1 - x^(21*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)
CROSSREFS
Sequence in context: A240016 A035970 A240017 * A240018 A035989 A240019
KEYWORD
nonn,easy
STATUS
approved